Magnetic field

Electric and Magnetic Fields

An electric field is generated around any electric charge, whether stationary or moving.
A magnetic field, represented by the symbol B, surrounds both moving electric charges and magnetic substances.

The magnetic force (FB) acting on a charged particle moving in a magnetic field is proportional to the charge (q) and the particle's speed (U).
The magnetic force's magnitude and direction depend on the velocity of the particle and the magnetic field's magnitude and direction.
If a charged particle moves parallel to the magnetic field, the magnetic force acting on it is zero.
When the velocity vector makes an angle (θ) with the magnetic field, the magnetic force acts perpendicularly to both the velocity (V) and the magnetic field (B).
The relationship is defined as: FB = q (V x B).

The magnetic force on a positive charge is opposite to that on a negative charge moving in the same direction.
The force can also be expressed as: FB = quB sin(θ), indicating the influence of the sine of the angle between V and B.
The right-hand rule can determine the direction of FB; if θ is positive, FB points upward, and if negative, it points downward.

Electric force acts along the electric field, while magnetic force is always perpendicular to the magnetic field.
Electric forces affect charged particles regardless of their motion; magnetic forces require motion.
The electric force does work on a charged particle, whereas magnetic forces do not do work in a steady magnetic field.

A magnetic field does not change the speed of a charged particle; it may alter the direction of its velocity but not its kinetic energy.
A charged particle in a uniform magnetic field with an initial velocity perpendicular to the field will move in a circular path.
The magnetic force (FB) is at a right angle to both V and B, maintaining a constant magnitude and changing direction, resulting in circular motion.
The angular speed of the particle does not depend on its linear speed or orbital radius and is associated with the cyclotron frequency.

J.J. Thomson used this understanding in 1897 to determine the charge-to-mass ratio (e/me) of electrons.

When a conductor carrying current is in a magnetic field, a potential difference arises perpendicular to both the current and the magnetic field. This phenomenon is known as the Hall effect, which reveals information about charge carriers' type and density, as well as magnetic field strength.

Isolated magnetic poles (monopoles) have yet to be discovered; magnetic field lines form closed loops.
The net magnetic flux through a closed surface around a magnetic pole is zero.

Materials can be categorized by their magnetic properties:
- Paramagnetic and ferromagnetic materials have permanent magnetic moments.
- Diamagnetic materials lack permanent magnetic moments.

Ferromagnetic materials exhibit strong magnetic effects and are made of domains with aligned magnetic moments. Examples include iron, cobalt, and nickel.
Domain walls separate regions of varying magnetic orientation.

Diamagnetic substances show a weak magnetic moment induced in the opposite direction of an external magnetic field, causing them to weaken or be repelled by magnets.

In the presence of a magnetic field, current-carrying conductors create potential differences. Ampere’s Law defines the relationship between current (I) and the magnetic field (B) around it.
The law holds for any closed integration path and any current distribution.

A solenoid consists of tightly packed loops of wire, resulting in a concentrated magnetic field within the solenoid and a weaker field outside.
The magnetic field inside a long solenoid is uniform and does not depend on the axial position if end effects are not considered.
A toroid loops back on itself, avoiding end effects, though the field is not constant throughout.

Numerical example: A 10-cm long solenoid with 400 turns carrying 2 A current demonstrates how to calculate the magnetic field inside.